I have this table of variables, they can have the following values:
$v_1 \in \{1,2\}$,
$v_2 \in \{1,2,3\}$,
$v_3 \in \{1,2,3,4\}$,
I need to generate all the possible combinations $v_1v_2v_3$ of these variables. Using this example it'll be $24$ possible combinations: $111, 112, 113, 114, 212, 213, 214$, and so on. But I need to obtain a sample of these combinations, instead of being $24$ combinations I need $10$, the thing I need is to retrieve a proportional sample, not completely random results, but to give a specific weight to each variable. What would be the best way to obtain this value?